Umberto Biccari – cmc.deusto.eus

Spiking Neural Networks: a theoretical framework for Universal Approximation and training

U. Biccari (2025) Spiking Neural Networks: a theoretical framework for Universal Approximation and training Abstract. Spiking Neural Networks (SNNs) are widely regarded as a biologically-inspired and energy-efficient alternative to classical…

Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels

K. Lyu, U. Biccari, J. Wang (2025) Robust stabilization of hyperbolic PDE-ODE systems via Neural Operator-approximated gain kernels Abstract. This paper investigates the mean square exponential stabilization problem for a…

A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints

Roberto Morales, U. Biccari (2025) A Multi-Objective Optimization framework for Decentralized Learning with coordination constraints, Abstract. This article introduces a generalized framework for Decentralized Learning formulated as a Multi-Objective Optimization…

Boundary observation and control for fractional heat and wave equations

U. Biccari, E. Zuazua (2025) Boundary observation and control for fractional heat and wave equations, https://doi.org/10.48550/arXiv.2504.17413 Abstract. We establish boundary observability and control for the fractional heat equation over arbitrary…

Gaussian Beam ansatz for finite difference wave equations

U. Biccari, E. Zuazua (2025) Gaussian Beam ansatz for finite difference wave equations, Found Comput Math. , Vol. 25, pp. 1–54, https://doi.org/10.1007/s10208-023-09632-9 Abstract. This work is concerned with the construction…

Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation

H. Antil, U. Biccari, R. Ponce, M. Warma, S. Zamorano (2024) Controllability properties from the exterior under positivity constraints for a 1-D fractional heat equation, Vol. 13, pp. 893-924, https://doi.org/10.3934/eect.2024010…

Multilevel control by duality

U. Biccari, E. Zuazua (2023) Multilevel control by duality Systems & Control Letters, Vol. 175, 105-502, https://doi.org/10.1016/j.sysconle.2023.105502 Abstract. We discuss the multilevel control problem for linear dynamical systems, consisting in designing…

A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation

U. Biccari, Y. Song, X. Yuan, E. Zuazua (2023) A Two-Stage Numerical Approach for the Sparse Initial Source Identification of a Diffusion-Advection Equation Inverse Problems, Vol. 39, No. 9, IP-103963,…

Multiplicity of solutions for fractional q(.)-Laplacian equations

A. Rahmoune, U. Biccari (2023) Multiplicity of solutions for fractional -Laplacian equations., J Elliptic Parabol Equ, Vol. 9, pp. 1101–1129, https://doi.org/10.1007/s41808-023-00239-3 Abstract. In this paper, we deal with the following elliptic…

Multilevel Selective Harmonic Modulation via Optimal Control

U. Biccari, C. Esteve-Yagüe, D.J. Oroya-Villalta (2022) Multilevel Selective Harmonic Modulation via Optimal Control., Appl Math Optim, Vol. 86, No. 43, https://doi.org/10.1007/s00245-022-09917-5 Abstract. We consider the Selective Harmonic Modulation (SHM) problem,…

Multilevel selective harmonic modulation by duality

U. Biccari, E. Zuazua Multilevel selective harmonic modulation by duality (2022) IFAC-PapersOnLine, Vol. 55, No. 16, pp. 56-61, https://doi.org/10.1016/j.ifacol.2022.08.081. Abstract. We address the Selective Harmonic Modulation (SHM) problem in power…

Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion

Y. Simporé, U. Biccari (2022) Controllability and Positivity Constraints in Population Dynamics with age, size Structuring and Diffusion Abstract. In this article, we consider the infinite dimensional linear control system…

Null Controllability for a Degenerate Structured Population Model

Y. Simporé, Y. El gantouh, U. Biccari (2022) Null Controllability for a Degenerate Structured Population Model Abstract. In this paper, we consider the infinite dimensional linear control system describing population…

Control and Numerical approximation of Fractional Diffusion Equations

Umberto Biccari, Mahamadi Warma, Enrique Zuazua. Control and Numerical approximation of Fractional Diffusion Equations (2022) Handb. Numer. Anal. Elsevier. ISSN:1570-8659, DOI: https://doi.org/10.1016/bs.hna.2021.12.001 Abstract. The aim of this work is to give…

Optimal control of linear non-local parabolic problems with an integral kernel

U. Biccari, V. Hernandez-Santamaria, L. Louison, A. Omrane. Optimal control of linear non-local parabolic problems with an integral kernel. (2021) Abstract. We consider a linear non-local heat equation in a bounded…

Blow-up results for a logarithmic pseudo-parabolic p(.)-Laplacian type equation

A. Rahmoune, U. Biccari (2021) Blow-up results for a logarithmic pseudo-parabolic -Laplacian equation. Abstract. In this paper, we consider an initial-boundary value problem for the following mixed pseudo-parabolic p(.)-Laplacian type equation…

Internal control for a non-local Schrödinger equation involving the fractional Laplace operator

U. Biccari Internal control for a non-local Schrödinger equation involving the fractional Laplace operator (2022), Vol. 11, No. 1: 301-324. doi: 10.3934/eect.2021014 Abstract: We analyze the interior controllability problem for…

A stochastic approach to the synchronization of coupled oscillators

Umberto Biccari, Enrique Zuazua. A stochastic approach to the synchronization of coupled oscillators. Frontiers in Energy Research, section Smart Grids. Front. Energy Res. Vol. 8 (2020). DOI: 10.3389/fenrg.2020.00115 Abstract. This paper…

Stochastic optimization methods for the simultaneous control of parameter-dependent systems

Umberto Biccari, Ana Navarro-Quiles, Enrique Zuazua. Stochastic optimization methods for the simultaneous control of parameter-dependent systems (2020) Abstract. We address the application of stochastic optimization methods for the simultaneous control of…

Controllability of the one-dimensional fractional heat equation under positivity constraints

U. Biccari, M. Warna, E. Zuazua Internal observability for coupled systems of linear partial differential equations. Commun. Pure Appl. Anal., Vol 19. No. 4 (2019), pp. 1949-1978. DOI: 10.3934/cppaa.2020086

Null-controllability properties of a fractional wave equation with a memory term

U. Biccari, M. Warma Null-controllability properties of a fractional wave equation with a memory term. Evol. Eq. Control The., Vol. 9, No. 2 (2020), pp. 399-430 Abstract: We study the…

Existence and cost of boundary controls for a degenerate/singular parabolic equation

U. Biccari, V. Hernandez-Santamaria, J. Vancostenoble. Existence and cost of boundary controls for a degenerate/singular parabolic equation (2022). Mathematical Control and Related Fields, Vol. 12, No.2, pp. 495-530, doi: 10.3934/mcrf.2021032…

Propagation of one and two-dimensional discrete waves under finite difference approximation

U. Biccari, A. Marica, E. Zuazua Propagation of one and two/dimensional discrete waves under finite difference approximation, Found. Comput. Math., Vol. 20 (2020), pp. 1401-1438. DOI: 10.1007/s10208-020-09445-0 Abstract: We analyze…

Model reduction of converter-dominated power systems by Singular Perturbation Theory

U. Biccari, N. Sakamoto, E. Unamuno, D. Madariaga, E. Zuazua, J.A. Barrena. Model reduction of converter-dominated power systems by Singular Perturbation Theory Abstract: The increasing integration of power electronic devices is driving the development of more advanced tools and methods for…

Null controllability of a nonlocal heat equation with an additive integral kernel

U. Biccari, V. Hernández-Santamaría Null controllability of a nonlocal heat equation with an additive integral kernel. SIAM J. Control Optim., Vol. 57, No. 4 (2019), pp. 2924-2938, DOI: 10.1137/18M1218431 Abstract:…

Null-controllability properties of the wave equation with a second order memory term

U. Biccari, S. Micu Null-controllability properties of the wave equation with a second order memory termJ DIFFER EQUATIONS, Vol. 267, No. 2 (2019), pp. 1376-1422 doi.org/10.1016/j.jde.2019.02.009 Abstract: We study the…

Dynamics and control for multi-agent networked systems: a finite difference approach

U. Biccari, D. Ko, E. Zuazua Dynamics and control for multi-agent networked systems: a finite difference approach. Math. Models Methods Appl. Sci., Vol. 29, No. 4 (2019), pp. 755–790. DOI:…

Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential

U. Biccari Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential, Math. Control Relat. F., Vol. 9, No. 1 (2019), pp. 191-219, DOI: 10.3934/mcrf.2019011 Abstract: We analyse…

The Poisson equation from non-local to local

U. Biccari, V. Hernández-Santamaría The Poisson equation from non-local to local, Electronic Journal of Differential Equations, Vol. 2018 (2018), No. 145, pp. 1-13. DOI: arXiv:1801.09470 Abstract: We analyze the limit…

Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects

U. Biccari, V. Hernández-Santamaría Controllability of a one-dimensional fractional heat equation: theoretical and numerical aspects, IMA J. Math. Control Inf., Vol. 36, No. 4 (2019), pp. 1199-1235. DOI: 10.1093/imamci/dny025 Abstract:…

Local regularity for fractional heat equations

U. Biccari, M. Warma, E. Zuazua Local regularity for fractional heat equations<, Recent Advances in PDEs: Analysis, Numerics and Control, SEMA SIMAI Springer Series, Vol. 17 (2018). DOI: 10.1007/978-3-319-97613-6 Abstract:…

Local elliptic regularity for the Dirichlet fractional Laplacian

U. Biccari, M. Warma, E. Zuazua Local elliptic regularity for the Dirichlet fractional Laplacian Advanced Nonlinear Studies, Vol. 17, Nr. 2 (2017), pp. 387-409. DOI: 10.1515/ans-2017-0014 Abstract: We analyze the…

Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian

U. Biccari, M. Warma, E. Zuazua Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian Adv. Nonlinear Stud., Vol. 17, Nr. 4 (2017), pp. 837-839. DOI: 10.1515/ans-2017-6020 Abstract: In [1],…

Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function

U. Biccari, E. Zuazua Null controllability for a heat equation with a singular inverse-square potential involving the distance to the boundary function J. Differential Equations, Vol. 261, No. 5 (2016),…